Advanced Function

Advanced function

Question 13

By; Nada and Ayah

2021-10-25

(B)Q13) A polynomial has a single root at x=1, a double root at x=-2 and two complex Roots at x= -2 + i and x= 1+i . If this polynomial has a y-intercept at (0,80) determine the equation of this polynomial

Our Question

procedure

The (x)

Calculations

x=1 x=-2 x=-2+i x= -2-i (Conjugate) x= 1+i x=1-i (Conjugate)

y=a(x+2-i)(x+2+i)(x-1-i)(x-1+i)(x-1)(x+2)^2 y=a([(x+2)^2 -i^2][(x-1)^2-i^2](x-1)(x+2)^2 y=a([(x+2)^2 +1][(x-1)^2+1](x-1)(x+2)^2 y=a([(x^2+4x+4)+1][(x^2-2x+1)+1](x-1)(x+2)^2 y=a((x^2+4x+5)(x^2-2x+2)(x-1)(x+2)^2

Final Eqaution

Finding (a)

For the function

For the function

Use (0,80) which is the y-intercept y=a(x-1)(x+2)^2(x^2-2x+2)(x^2+4x+5) We plugged in our y intercept as 80 and our (x) as zero 80=a(0-1)(0+2)^2(0^2-2(0)+2) (0^2+4(0)+5) 80=a(-1)(4)(2)(5) 80=a(-40) 80 =a -40 a= -2

By plugging our a=-2 we recive a final equation as y=-2(x-1)(x+2)^2(x^2-2x+2)(x^2+4x+5)

Thanks for you listening

Any question?